There are numerous situations which involve a workpiece being removed for example from a workpiece processing station by means of a gripping apparatus and possibly transported into another working station, or which involve a workpiece being fixed in a proper position, for example for a working operation to be carried out thereon. For such purposes the gripping apparatus may generally comprise a gripping device which can be set by means of an adjusting mechanism to the workpiece to be handled, so that the respective workpieces can be gripped with a specific gripping force which is such as to ensure that the workpiece is adequately held by the gripping device for example during the transportation operation.